Different configurations and shapes of transducer or loudspeaker arrays for outputting one or more audio signals are known from the related art. WO2011/144499 A1, for instance, discloses a circular loudspeaker array mounted on a cylindrical body. By processing the audio signal in a suitable manner the directivity of the circular loudspeaker array disclosed in WO2011/144499 A1 can be controlled. This process is usually called beamforming.
In the majority of cases, for circular and spherical loudspeaker arrays, beamforming is based on the so-called “mode-matching” approach. The objective is to generate a sound beam with a circular loudspeaker array mounted on a cylindrical body. The array consists of L loudspeakers flush-mounted on the surface of a rigid (ideally infinite) cylinder at the same height. The angular spacing between loudspeakers is assumed to be uniform. The signal ql(ω) driving the l-th loudspeaker at angular coordinate ϕl, that is required to generate a sound beam steered towards direction ϕ0, is given by the following expression (in the frequency domain):ql(ω)=X(ω)Σn=−NNein(ϕl−ϕ0)Cn(ω),  (1)where X(ω) is the mono audio input signal associated with the sound beam, N is a parameter that controls the width of the beam, i is the imaginary unit and Cn(ω) is a frequency dependent function that depends on the radius of the cylinder and on the characteristic of the loudspeakers. The coefficients Cn(ω) are generally obtained from the analytical expression of the sound field radiated by a rectangular piston on an infinite and rigid cylindrical baffle (M. Kolundzija, C. Faller, and M. Vetterli, “Design of a Compact Cylindrical Loudspeaker Array for Spatial Sound Reproduction”, AES 130th Cony., 2011; M. Moller, M. Olsen, F. Agerkvist, J. Dyreby, and G. Munch, “Circular loudspeaker array with controllable directivity”, in Audio Engineering Society Convention 128, 2010). A more advanced but similar expression was derived that accounts also for the finite height of the rigid cylinder (H. Teutsch and W. Kellermann, “Acoustic source detection and localization based on wavefield decomposition using circular microphone arrays”, Journal of the Acoustical Society of America, vol. 120, pp. 2724-2736, November 2006).